Ultrasensitive differential microcalorimeter

ABSTRACT

A calorimeter includes sample and reference cells, a thermal shield surrounding these cells, a heating device thermally coupled to the thermal shield, temperature sensors for monitoring a temperature of the shield and a temperature differential between the shield and the cells, and a control system. The control system has an output line connected to the heating device and input lines to receive signals from the temperature sensors. The control system is configured to generate on its output line an output signal which is a function of both the input signals received on its input lines.

BACKGROUND OF THE INVENTION

This invention relates generally to microcalorimeters and morespecifically to features that improve the performance of ultrasensitivemicrocalorimeters.

Ultrasensitive microcalorimeters are broadly utilized in fields ofbiochemistry, pharmacology, cell biology, and others. Calorimetryprovides a direct method for measuring changes in thermodynamicproperties of biological macromolecules. Ultrasensitivemicrocalorimeters are typically twin cell instruments in whichproperties of a dilute solution of test substance in an aqueous bufferin a sample cell is continuously compared to an equal quantity ofaqueous buffer in a reference cell. Measured differences between theproperties of two cells, such as temperature or heat capacity, can beattributed to the presence of the test substance in the sample cell.

There are two popular types of microcalorimeters, namely, a differentialscanning microcalorimeter and an isothermal titration calorimeter. Thedifferential scanning calorimeter automatically raises or lowers thetemperature at a given rate while monitoring the temperaturedifferential between cells. From the temperature differentialinformation, small differences in the heat capacities between the samplecell and the reference cell can be determined and attributed to the testsubstance. One of the popular uses of scanning calorimetry is to measurethe thermodynamic properties for thermally-induced structuraltransitions of biopolymers in very dilute solutions, where approximately0.1% of the mass of solution is the biopolymer itself and more than99.9% is the solvent. Even using the differential method, scanningcalorimeters must have extremely high sensitivity in order to measureproperties of the biopolymer in the presence of an overwhelming amountof the aqueous solution.

The isothermal titration calorimeter (ITC) is also a twin-celldifferential device, but operates at a fixed temperature while theliquid in the sample cell is continuously stirred. The most popularapplication for titration calorimetry is in the characterization of thethermodynamics of molecular interactions. In this application, a dilutesolution of the test substance (e.g., a protein) is placed in the samplecell and, at various times, small volumes of a second dilute solutioncontaining a ligand which binds to the test substance are injected intothe sample Cell. The instrument measures the heat which is evolved orabsorbed as a result of the binding of the newly-introduced ligand tothe test substance. From results of multiple-injection experiments, thebinding constant, heat of binding, and stoichiometry of binding can bedetermined.

The sensitivity of either type of microcalorimeter is limited by heatexchange between the cells and its surroundings. When there is no heatexchange between the cells and the surroundings, the microcalorimeter isadiabatic. In order to limit uncontrolled heat exchange between thecells and the ambient environment, the cells are surrounded by a thermalshield containing controlled heating and cooling means. The thermalshield has a thermocouple-activated sensor which measures differentialtemperature between the shield and the cells. When this temperaturedifferential is minimized, heat exchange between the cells and shield isalso minimized.

Scanning differential microcalorimeters generally operate in one of twomodes: adiabatic and non-adiabatic. In the adiabatic mode, thetemperature of the cells is driven at a constant rate and thetemperature of the thermal shield is maintained equal to the temperatureof the cells by a differential control system. Measurement of thetemperature differential between the shield and cells goes to an inputof a high-sensitivity amplifier and then to a controller. The controllerheats and/or cools the shield to balance the temperature between theshield and the cells. The benefit of the adiabatic mode is highsensitivity resulting from minimal heat exchange between cells andshield. However, since the cells cannot be directly cooled, thosecalorimeters which upscan (heat cells) in the adiabatic mode mustdownscan (cool cells) using the non-adiabatic mode. Also, when desiringto operate in an adiabatic mode at constant temperature, constancy intemperature is difficult to maintain for long periods of time.

In the non-adiabatic mode, the temperature change of the shield followsa prespecified path and the temperature of the cells follow that of theshield through heat conduction. Typically, the actual temperature of theshield is repeatedly measured and compared to the desired temperature.Differences between these two temperatures are used to actively modifythe heating and cooling of the shield. Since heat conduction betweencells and shield is slow, the temperature of the cells can lag thetemperature of the thermal shield by 5° C. or more at scanning rates of60°-120° C./hr. A benefit of this type of calorimeter is that heating orcooling of the cells is possible using the same mode of operation.Another advantage is that when operating at constant temperature, thereis very little temperature drift even over long periods of time.However, the non-adiabatic mode has several drawbacks, the mostimportant being that it is less sensitive than the adiabatic mode ofoperation. First, its sensitivity is limited by the inability touniformly control the temperature of the shield, and second, thebaseline is difficult to reproduce from scan to scan due to the veryhigh heat leak from the cells to the shield.

Microcalorimeters typically compensate for differential heat effectsbetween the two cells by one of two methods: passive compensation oractive compensation. In microcalorimeters using passive compensation,temperature differences arising from heat events dissipate due todifferential heat flow between the two cells. In microcalorimeters usingactive compensation, temperature differentials between the two cellsactivate a power feedback system which supplies appropriate heatdirectly to the cooler cell. Actively heating the cooler cell occurs inaddition to differential heat flow, thereby more quickly reducingtemperature differences between cells. The primary advantage of activecompensation is the much shorter time required to equilibrate the twocells, resulting in a fast instrument response time. The primarydisadvantage is that the feedback system generates noise and-baselineirregularity over and above that exhibited with passive compensation.

SUMMARY OF THE INVENTION

In general, in one aspect, the invention is a calorimeter which includessample and reference cells, a thermal shield surrounding these cells, aheating device thermally coupled to the thermal shield, temperaturesensors for monitoring a temperature of the shield and a temperaturedifferential between the shield and the cells, and a control system. Thecontrol system has an output line connected to the heating device andinput lines to receive signals from the temperature sensors. The controlsystem is configured to generate on its output line an output signalwhich is a function of both the input signals received on its inputlines.

In preferred embodiments, the control system includes a memory whichstores a mapping function. The mapping function maps the temperature ofthe thermal shield, which is monitored by the first temperature sensor,to a correction term. The control system combines this correction termwith the second signal from the temperature differential sensor togenerate the output signal to the heating device for the thermal shield.

In general, in another aspect, the invention is a calorimeter whichincludes sample and reference cells, a thermal shield surrounding thecells, a heating device thermally coupled to both of the cells, atemperature monitoring system which monitors the temperature of at leastone of the cells, and a control system which during operation causes theheating device to heat both the sample and reference cells at auser-selected scan rate. The control system has an output line connectedto the heating device and an input line which receives a signal from thetemperature monitoring system. The control system is configured togenerate on its output line an output signal which is a function of botha user-selected scan rate and the signal on the input line.

In preferred embodiments, the control system includes a memory storing amapping function which maps both the monitored temperature and theuser-selected scan rate to a control parameter. The control systemgenerates an output signal on the output line that is derived from thecontrol parameter and is sent to the heating device.

In general, in still another aspect, the invention is a method ofgenerating a mapping function for producing improved adiabaticperformance of a calorimeter. The method includes the steps of (a)choosing a plurality of temperatures within a range of temperatures; (b)heating the sample cell in the calorimeter to a selected one of theplurality of temperatures; (c) heating the thermal shield so as tominimize a temperature differential between the sample cell and thethermal shield; (d) when a temperature of the calorimeter reaches theselected temperature, discontinuing the heating of the sample cell; (e)recording a drift in the temperature of the calorimeter over a period oftime; (f) determining a correction term for the selected temperaturewhich minimizes the drift in the temperature; (g) repeating steps (b-f)for the rest of the plurality of temperatures; and (h) deriving themapping function from the correction terms for the plurality oftemperatures.

In preferred embodiments the method further includes fitting apolynomial to the correction terms for the plurality of temperatures,wherein the polynomial is the mapping function.

In general, in a further aspect, the invention is a method of generatinga mapping function for producing a more constant scan rate in acalorimeter. The method includes the steps of: (a) selecting a scan ratewithin a range of scan rates; (b) heating the sample cell so that itstemperature changes at a rate that is determined by the selected scanrate; (c) recording the temperature of the sample cell as a function oftime to determine a measured scan rate for the sample cell; (d) from therecorded temperature, determining an actual scan rate at a plurality oftemperatures; and (e) based upon an amount by which the actual scan ratediffers from the selected scan rate, determining for the selected scanrate a correction term at each of the plurality of temperatures whichwhen applied to the step of heating the sample cell produces an actualscan rate for the cell that is more constant over temperature than themeasured scan rate, wherein the mapping function is derived from thecorrection terms.

In preferred embodiments the method may include one or more of thefollowing features. The method may further includes the steps of: (f)performing steps (b-e) for a plurality of different selected scan rateswithin the range of scan rates. In addition, the method may furtherinclude generating the mapping function from the correction terms forthe plurality of scan rates and the plurality of temperatures at eachscan rate. The method may also include the step of (f) fitting apolynomial to the correction terms that were obtained at the pluralityof temperatures for the selected scan rate. The method may also includethe step (f) for performing steps (b-e) for a plurality of differentselected scan rates within the range of scan rates to arrive at aplurality of polynomials, one for each of said plurality of scan rates.In addition, the method may further include the step in which for acorresponding term of each of the plurality of polynomials, fitting asecond polynomial to coefficients of those corresponding terms so thatthe second polynomial expresses the coefficient as a function of scanrate.

In general, in still a further aspect, the invention is a differentialcalorimeter including sample and reference cells, a first heating devicethermally coupled to the sample cell, a second heating device thermallycoupled to the reference cell, a temperature sensor which monitors atemperature differential between sample and reference cells, and acontrol system. The control system has an output line connected to atleast one of said heating devices, an input line connected to thetemperature sensor, and an user-interface. The user-interface permittinga user-selected gain setting, wherein the control system is configuredto provide on its output line an output signal which is given by theproduct of the user-selected gain setting and the temperaturedifferential from the input line.

Other advantages and features of the invention will become apparent fromthe following description of the preferred embodiment and from theclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic of the differential microcalorimeterinstrument;

FIG. 2 shows a flow diagram of the method for determining thetemperature-dependent equation that provides improved adiabaticity;

FIG. 3 shows a typical plot of scan rate versus temperature for aconstant voltage applied to the cell heaters;

FIG. 4 shows a flow diagram of the method for determining the equationthat improves scan-rate constancy.

DESCRIPTION OF THE INVENTION

A schematic diagram of an embodiment of the improved differentialmicrocalorimeter is shown in FIG. 1. There are two cells, a referencecell 1 and a sample cell 2, each identical in volume and mass, andassembled with inlet capillary tubes and matched heating elements 3 and4. These cells are of the total-fill type, with the test liquidoccupying the entire volume of each cell and capillary tube. The heatingelements 3 and 4 are driven by a power source 5 which is controlled by acomputer 6. The computer includes a interface 40, so that the user mayinput specifications, and a memory 30 for storage, for example, a harddrive or random access memory. The heating elements 3 and 4 are matchedand driven simultaneously by power source 5, so cells 1 and 2 are heatedat an identical rate, which is controlled by the computer. The rate atwhich the temperature of the cells changes is referred to as the scanrate and is specified by the user through the computer-interface 40. Athermal effect measuring device 7 is connected to a sensor 8 thatmeasures the difference in temperature between the two cells. Typicalsensors include wire thermocouples or semiconducting thermocouples. Thetemperature differential is measured periodically as the cells are beingheated during a scan. The temperature differential data is then sentfrom thermal effect measuring device 7 to computer 6, where it is savedalong with the time of the measurement in the computer memory 30.

The cells 1 and 2 are surrounded by a thermal shield 9. During adiabaticoperation, the shield helps minimize heat exchange between the cells andtheir surroundings. The temperature of thermal shield 9 is monitored byan absolute temperature measuring device 13 which is activated by asensor 14 (typically a platinum resistance thermometer device or RTD)which is mounted on the thermal shield. Thermal shield 9 is connected toa heating and cooling device 10 (typically an array of Peltier devices)which is operated by a controller 11. The signal to the controller 11comes from the output of a summing amplifier 15 which receives twoinputs. The first input 20 receives its signal from sensor 12 thatmonitors the difference between the temperature of thermal shield 9 andthe average temperature of the two cells 1 and 2. The second input 16receives its signal from a power source 17 whose output is controlled bycomputer 6. The output from absolute temperature measuring device 13 issent to computer 6 and used to determine the appropriate signal to sendto power source 17 and subsequently onto the summing amplifier 15. Theabsolute temperature information is repeatedly stored in the computermemory 30 in conjunction with the temperature differential between cellsand the time of the measurement. The operating range for the calorimeterin terms of the temperature at which the cells and shield can beoperated is -20° C. to 150° C.

Additional cell heaters 18 and 19 are located on reference and samplecells 1 and 2, respectively. The power to each of these heaters isindependently controlled directly by the output of computer 6. Thesecell heaters 18 and 19, which generate only small amounts of heat, areused to actively reduce any temperature differential between cells.Through the computer interface 40, the user can select between passivecompensation, in which additional heaters 18 and 19 are not used, orvarious levels (typically low, medium, and high) of active compensation,in which these additional heaters are used by computer 6 to activelyminimize the temperature differential between cells 1 and 2. The choiceof passive compensation or various levels of active compensation isequivalent to a selection between a number of instrument response times.

Improvement of Adiabatic Operation

The calorimeter can operate in one of three modes: adiabatic, improvedadiabatic, and non-adiabatic. Selection of a particular mode ofoperation is made through computer interface 40. In the adiabatic mode,the second input 16 to the summing amplifier 15 is deactivated. Asdescribed previously, the first input 20 of the summing amplifierreceives a signal from sensor 12 which monitors the difference betweenthe temperature of thermal shield 9 and the average temperature of thetwo cells 1 and 2. Based only on the temperature differential signalreceived at the first input 20, the summing amplifier 15 sends a signalto controller 11. In turn, controller 11 regulates heating and coolingdevice 10 for thermal shield 9 in relation to the signal from summingamplifier 15, thereby minimizing the temperature difference betweenshield 9 and the cells 1 and 2. In this way, the temperature of thermalshield 9 follows the temperature of the cells 1 and 2, which iscontrolled by computer 6 via power source 5 and cell heaters 3 and 4.

However, the adiabatic mode of operation does not provide completelyadiabatic performance. For example, if cells 1 and 2 are raised to atemperature above room temperature and then cell heaters 3 and 4 areturned off, but the calorimeter remains in the adiabatic mode, thedifferential temperature between the shield and the cells will continueto be actively minimized as described above. It is observed empirically,however, that the absolute temperature of the cells and shield willdrift downward. The rate of this temperature drift can approach 1-2°C./hour when the temperature of the calorimeter is about 70° C. If thecalorimeter performed adiabatically, no drift in temperature would beobserved.

To improve adiabatic performance, the calorimeter can operate in theimproved adiabatic mode. In this mode of operation, both inputs tosumming amplifier 15 are activated. In addition to the signal receivedat the first input 20 from the differential temperature sensor 12,summing amplifier 15 receives a second signal at the second input 16from computer 6 via power source 17. This second signal represents acorrection factor generated by an empirically-derived equation which isstored in computer memory 30. The correction factor is a function of thecurrent temperature of thermal shield 9 which is repeatedly measured andstored in computer memory 30 during operation. The two signals receivedby summing amplifier 15, i.e. the signal from the differentialtemperature sensor 12 and the correction factor, are added together andsent to controller 11 which regulates the heating and cooling device 10accordingly. More generally, any summing circuit may be used whichfunctionally combines the two input signals, whether by simple additionor by some other operation.

The correction factor is repeatedly recomputed and revised as the cellsare being heated during a scan or as they are being maintained at aparticular temperature. The correction factor attempts to compensate forfactors that limit adiabatic performance, such as heat exchange betweenthe shield and the surroundings and temperature gradients within thecalorimeter.

The calorimeter can also operate in a non-adiabatic mode. In this case,the cell heaters 3 and 4 are deactivated. The signal from computer 6 tothe second input 16 of summing amplifier 15, via second power source 17,gives a specified rate of heating and cooling thermal shield asdetermined by a file specified by the user through computer interface 40and stored in computer memory 30. The file is a function of thetemperature of thermal shield 9 which is measured repeatedly during thescan. A signal is sent from summing amplifier 15 to controller 11 whichin turn regulates heating and cooling device 10 accordingly. In thiscase, the temperature of the cells 1 and 2 follow the temperature ofthermal shield 9 by heat conduction. Since the heat conduction processis relatively slow, the temperature of the cells typically lags behindthe temperature of the thermal shield, in contrast to the former twocases where the temperature of the thermal shield is actively driven tofollow the temperature of the cells.

Determination of Equation for Improved Adiabatic Operation

The empirically-derived equation which gives the correction factor forimproved adiabaticity is determined in a manner shown in FIG. 2. Aplurality of temperatures within a range of temperatures are selected.The temperature range should span the scanning range of the instrument,typically, -20° C. to 150° C., and the temperatures within the rangeshould be spaced sufficiently close together, e.g. every 5° C., so thecorrect signal at intermediate temperatures can be accuratelyinterpolated (step 100). Cells 1 and 2 are filled with a standardliquid, typically water, and allowed to equilibrate thermally for ashort time prior to the start of scanning (step 102). The lowesttemperature is selected to begin the calibration run (step 104). Theentire apparatus is brought to an initial temperature below the selectedtemperature by heating or cooling thermal shield 9 using thenon-adiabatic mode of operation (step 106). Then a temperature upscan isstarted by supplying a given constant voltage from power supply 5 tocell heaters 3 and 4, which heats the cells at a nearly constant rate.The upscan is initiated using the adiabatic mode of operation so thetemperature of the thermal shield is made to follow the averagetemperature of the cells 1 and 2 (step 108). Once the temperature ofthermal shield 9, which is monitored, reaches the selected temperature,the power to cell heaters 3 and 4 is shut off (step 110). The instrumentstill in the adiabatic mode, the difference between the temperature ofthermal shield 9 and the average temperature of the two cells 1 and 2 isactively minimized. The absolute temperature of thermal shield 9 isperiodically measured and recorded (step 112).

The temperature of the shield will tend to drift toward room temperaturereflecting heat exchange from the cells to the surroundings via theshield. Using the temperature drift data collected in step 112 andknowledge of the heat capacity of thermal shield 9 and cells 1 and 2,the rate of heat exchange between the calorimeter and the surroundingsis then determined (step 114). Knowing the rate determined in step 114and the heating and cooling characteristics of device 10, enables one tothen compute a correction which must be sent to controller 11 tocompensate for the heat exchange between the calorimeter and thesurroundings and eliminate the temperature drift. This corrected voltageis sent to the second input 16 of summing amplifier 15 from computer 6via power source 17 (step 116).

The temperature of thermal shield 9 is again measured as a function oftime. If it does not remain substantially constant, the signal to thesecond input 16 of summing amplifier 15 is iteratively modified from theinitial result until the measured temperature of the shield remainssubstantially constant. This final signal is recorded and stored incomputer memory 30 along with the temperature (step 118).

Steps 100-118 are then repeated for each of the remaining temperaturesselected in step 100 (step 120). When calibrations are completed for alltemperatures, the resulting data represents a correction factor as afunction of temperature. A temperature-dependent polynomial equation isfitted to the recorded data using standard non-linear least-squaresregression techniques (step 122).

Improving Constancy of Scan Rate

During adiabatic or improved adiabatic modes of operation, theinstrument produces improved constancy of scan rate. When power supply 5provides a constant voltage to cell heaters 3 and 4, the temperaturechange in the cells 1 and 2 will initially rise linearly with time. Thisinitial scan rate is referred to as the nominal scan rate. As thetemperature rises, however, the current scan rate will diverge from thenominal scan rate. These deviations arise due to various factorsincluding for example temperature-dependent resistivity of cell heaters3 and 4, the temperature-dependent heat capacity of cells 1 and 2 andtheir contents, and departures from adiabatic operation. FIG. 3illustrates the typical departure from a constant scan rate for aparticular constant voltage. To produce a constant scan rate, computer 6via the power source 5 sends a variable voltage to cell heaters 3 and 4as determined by a second empirically-derived equation. This equationdepends functionally on the desired scan rate, which is specified by theuser prior to the scan through computer interface 40, and thetemperature of thermal shield 9. In other words, the voltage signal tocell heaters 3 and 4 is updated repeatedly based on the measuredtemperature of thermal shield 9.

Equation for Improved Constancy of Scan Rate

The second equation which provides improved constancy of scan rate isdetermined empirically using the method shown in FIG. 4. The userselects a number of desired scan rates which span the range of scanrates that the user intends to employ. The selected scan rates arespaced close enough together that the correct voltage values can beinterpolated for intermediate desired scan rates (step 200). The userthen selects a temperature range which spans the temperature over whichthe instrument will be used. To perform the calibration, cells 1 and 2are first filled with a standard liquid. (step 202). From the scan ratesselected in step 200, a particular scan rate is selected (step 204).Using the non-adiabatic mode of operation, thermal shield 9 is cooledsuch that the temperatures of thermal shield 9 and cells 1 and 2 are atthe lowest temperature in the temperature range selected in step 202(step 206). Using knowledge of the temperature-dependent resistance ofcell heaters 3 and 4 and the heat capacity of cells 1 and 2 and theircontents, the constant voltage required to produce the selected scanrate at the current temperature is determined (step 208). Then, theconstant voltage determined in step 208 is supplied to cell heaters 3and 4 and the instrument is operated in the improved adiabatic mode(step 210). As the cells are being heated, the temperature of thermalshield 9 is measured as a function of time at intervals of, typically,five to one hundred seconds (step 212). Using the data from step 212,the actual scan rate as a function of temperature is computed.

By measuring the difference between actual scan rate and the nominalscan rate at each temperature, and by knowing the temperature-dependentresistance of cell heaters 3 and 4 and the heat capacity of cells 1 and2 and their contents, a voltage correction can be computed for eachtemperature for which data was taken. The corrected voltage, whenapplied to the heaters, will produce a scan rate which more closelyapproaches the nominal scan rate (step 214).

To further improve the voltage correction, the scan is repeated usingthe corrected voltages determined in step 214. The voltage correctionsare then iteratively modified until the desired rate of scan constancyis achieved. The final voltage as a function of temperature is recordedand stored to computer memory 30 over the temperature range selected instep 202 (step 216).

A temperature-dependent polynomial equation is fit to the voltage Vversus temperature T data from step 216 using standard non-linearleast-squares regression techniques. The equation is parametrized by theparticular scan rate r_(i) selected in step 204. The equation is shownin (1):

    V(r.sub.i,T)=a.sub.i +b.sub.i T+c.sub.i T.sup.2 +d.sub.i T.sup.3 +(1).

The fit provides values for coefficients a_(i), b_(i), c_(i), d_(i), . .. , which give the dependence of the function V(r_(i),T) on a particularorder of temperature T for the selected scan rate r_(i) (step 218).

Steps 204-218 are repeated for each scan rate selected in step 200 (step220). Once calibrations are completed for all scan rates, coefficientsdetermined in step 218 are grouped together according to the order oftemperature to which they apply. From this data, the set of coefficientsfor a particular order of temperature can be fit to a polynomialequation in scan rate r using standard non-linear least-squares methods:

    a=C.sub.1a +C.sub.2a r+C.sub.3a r.sup.2 +                  (2a)

    b=C.sub.1b +C.sub.2b r+C.sub.3b r.sup.2 +                  (2b)

After this exercise is completed, the set of equations (2a), (2b), . . ., can be substituted into equation (3) below:

    V(r,T)=a(r)+b(r)T+c(r) T.sup.2 +d(r)T.sup.3 +              (3)

yielding a single equation that gives voltage as a function oftemperature and desired scan rate (step 222).

The equation derived by the above method depends on the heat capacity ofthe test solution in the cells. Water is the most appropriate testsolution for calibration, since most experiments are carried out usingaqueous solutions. Experiments using non-aqueous solvents can beaccommodated by repeating the method above with the appropriate testsolution.

User-Selectable Response Time

The instrument allows the user to select, through computer interface 40,among a number of instrument response times. The instrument responsetime characterizes the rate of thermal equilibration between referencecell 1 and sample cell 2. A heat-producing event which occurs in onecell and not the other, will produce a temperature differential betweencells. The temperature differential will dissipate over time as a resultof thermal conduction between cells, i.e. passive compensation. Theadditional cell heaters 18 and 19 can be used to increase the rate ofthermal equilibration between cells by heating cells differently inorder to minimize the temperature differential between them, i.e. activecompensation.

The different choices of response time for this instrument are typicallyin the range of three to thirty-five seconds. Selection of the longestresponse time corresponds to passive compensation, in which theadditional cell heaters 18 and 19 are not used. Shorter response timesrequire active compensation and correspond to a particular gain settingin the computer. The computer multiplies the gain setting by themeasured temperature differential between cells to determine thevoltages used to differentially heat cell heaters 18 and 19.

During active compensation the instrument operates as follows. Cellheaters 3 and 4, which are controlled by computer 6 via power source 5,initiate a scan by heating cells 1 and 2 at a specified rate. Inaddition, a small constant voltage is applied to cell heater 18 which isconnected to reference cell 1. Because cell heater 18 provides aconstant voltage to reference cell 1, sample cell 2 can be heated orcooled relative to reference cell 1 by adjusting the voltage to cellheater 19. When a temperature in the cells is reached that triggers aheat producing event (or possibly a heat absorbing event) in sample cell2, a temperature differential is measured by sensor 8 and transmitted tocomputer 6 via thermal effect analyzer 7. The computer multiplies thisoff-balance signal by the user-selectable gain setting to proportionallyadjusts the voltage to cell heater 19 to drive the temperaturedifferential to zero. Measurement of the temperature differentialbetween cells and subsequent adjustment of the voltage to cell heater 19occur repeatedly throughout the scan. In this way, the temperaturedifferential between cells is actively minimized.

Use of a larger gain setting will produce a shorter response time.However, if the gain setting is too large, the differential heatingbetween cell heaters 18 and 19 will be too large, and the temperature ofthe sample cell will overshoot the temperature of the reference cell,thereby introducing oscillations in the temperature differential datathat is being saved to computer memory 30. The onset of theseoscillations provide the upper bound on the maximum gain setting andtherefore the lower bound for the shortest selectable instrumentresponse time.

During a scan, time, temperature, and temperature differential betweencells are repeatedly being stored to computer memory 30. The temperaturedifferential data at each temperature is usually converted to a powerdifferential that quantifies heat producing events at that temperaturefrom constituents in sample cell 2 that are not present in referencecell 1. This conversion depends on the selection of response time andthe correct conversion factors are stored in the computer memory 30prior to operation.

Determinations of the correct factors to convert a temperaturedifferential between cells to a power differential between cells iswell-known in the art and include the following calibration. The cells 1and 2 are filled with identical liquids, typically water, and allowed toequilibrate. At this time the temperature differential between cells hasa null baseline. Thereafter, a known increase (or decrease) in constantpower is imparted by reference cell heater 18 to reference cell 1. Thiswill cause the temperature of reference cell 1 to rise relative to thetemperature of sample cell 2. The temperature will not riseindefinitely, however, because of increased thermal conduction fromreference cell 1 to sample cell 2, i.e. passive compensation. Inaddition, if active compensation is selected, the sample cell 2 will beheated by cell heater 19 in proportion to the product of the gainsetting and the current temperature differential. The temperaturedifferential will increase until the heat produced by cell heater 18 toreference cell 1 is offset by the combination of passive and activecompensation which provide heat flow into the sample cell 2. Therefore,the temperature differential starts at a null baseline and rises, over aperiod of time, to a new non-zero baseline, subsequent to a constantpower differential being externally applied to reference cell 1. Theperiod of time over which the temperature differential rises quantifiesthe response time for a particular gain setting. One measure is thereferred to as the response half-time, which is the time it takes forthe temperature differential to go from the null baseline to a pointhalf-way in between the null baseline and the final non-zero baseline.The total measured change in temperature differential produced by theknown power differential gives the conversion factor between thesequantities for a particular selection of response time. Duringsubsequent operation, the measured temperature differential can beconverted to the correct power differential using theempirically-determined conversion factor for the appropriate responsetime setting.

The conversion factors can also be determined using a slightly differentcalibration method. In this case, the known power differential to thereference cell 1 is maintained only for a short period of time, and ineffect a heat pulse of known total energy is imparted to the referencecell. This will produce a transient in the temperature differentialdata. From the integrated area under the transient, relative to thebaseline, the correct conversion factor can be determined for each gainsetting.

Other embodiments are also within the scope of the invention. Forexample, in the above description the temperature of the cells wasdetermined by adding the temperature of the thermal shield to thetemperature differential between the cells and the shield, both of whichare measured. Alternatively, the temperature of the cells may bemeasured with a different combination of temperature sensors or thetemperature of the calorimeter can be measured at other locations withinthe system. In addition, the improved adiabatic mode of operation can beapplied to an isothermal titration calorimeter, or other types ofisothermal calorimeters, or also, to a scanning calorimeter operating inan isothermal mode. In these cases, the temperature of the cells isbrought to a selected temperature and thereafter the temperature is madeto remain constant by operating in the improved adiabatic mode withoutany voltage to cell heaters 3 and 4. Furthermore, theempirically-determined transformations for improving adiabatic operationand improving scan rate constancy, need not be represented by equations.Rather, the transformation could be represented, for example, by neuralnetwork or table of values from which intermediate values areinterpolated.

Other embodiments of the design include cells without filling tubes,cells which are removable from the inside of the shield, or a multilayerthermal shield.

What is claimed is:
 1. A calorimeter comprising:a sample cell; areference cell; a thermal shield surrounding said sample and referencecells; a heating device thermally coupled to the thermal shield; a firsttemperature sensor which monitors a temperature of the thermal shield; asecond temperature sensor which monitors a temperature differentialbetween the thermal shield and at least one of the sample and referencecells; a control system which has an output line connected to theheating device and which has a first input line and a second input line,wherein the first temperature sensor supplies a first signal to thefirst input line, the second temperature sensor supplies a second signalto the second input line, and wherein the control system is configuredto generate on its output line an output signal which is a function ofboth the first and second signals.
 2. The calorimeter of claim 1,wherein the control system includes a memory storing a mapping functionwhich maps the temperature of the thermal shield to a correction termand wherein the control system combines the correction term with thesecond signal to generate the output signal.
 3. The calorimeter of claim2, wherein the stored mapping function comprises a polynomial equation.4. The calorimeter of claim 2, wherein the stored mapping functioncomprises a table associating each of a plurality of temperatures with acorresponding correction factor.
 5. The calorimeter of claim 1, furthercomprising a heating unit which is thermally coupled to the sample andreference cells and which serves to establish during operation atemperature scan rate for the calorimeter.
 6. The calorimeter of claim5, further comprising a power source connected to said heating unit andcontrolled by the control system.
 7. The calorimeter of claim 5, whereinsaid heating unit comprises a first element associated with the samplecell and a second element associated with the reference cell, whereinsaid first and second elements are connected in series across an outputof said power source.
 8. The calorimeter of claim 1 wherein said controlsystem comprises a combining circuit which receives said second signaland a signal derived from the first signal and generates a combinedsignal therefrom, and wherein the control system generates said outputsignal from the combined signal.
 9. The calorimeter of claim 8 whereinsaid combining circuit is a summing circuit which adds said secondsignal and said derived signal to generate said combined signal.
 10. Thecalorimeter of claim 1 wherein said first temperature sensor comprises aresistor thermometer device.
 11. The calorimeter of claim 1 wherein saidsecond temperature sensor comprises a thermocouple.
 12. The calorimeterof claim 1 wherein said heating device is a heating and cooling device.13. The calorimeter of claim 1 further comprising a heating unit whichis thermally coupled to the sample and reference cells and which servesto establish during operation a temperature scan rate for thecalorimeter, wherein said control system during operation causes theheating unit to heat both the sample and reference cells at auser-selected scan rate, said control system having a second output lineconnected to the heating unit, and wherein the control system isconfigured to generate on its second output line an output signal whichis a function of both a user-selected scan rate and said first signal.14. The calorimeter of claim 13, wherein the control system includes amemory storing a mapping function which maps both the monitoredtemperature of the thermal shield and the user-selected scan rate to acontrol parameter and wherein the control system derives the outputsignal on the second output line from said control parameter.
 15. Thecalorimeter of claim 1, wherein the control system comprises a memorystoring a mapping function which maps an input value to a correctionterm and wherein the control system uses the mapping function to convertthe first input signal to a corresponding correction term and thengenerates the output signal from the second input signal and thecorresponding correction term.
 16. The calorimeter of claim 1, whereinthe control system comprises a converter which maps an input value to acorrection term and wherein the control system uses the converter toconvert the first input signal to a corresponding correction term andthen generates the output signal from the second input signal and thecorresponding correction term.
 17. The calorimeter of claim 1, whereinthe second temperature sensor monitors a temperature differentialbetween a temperature of the thermal shield and an average temperatureof the sample and reference cells.